Recently, attention has been focussed on the mathematics learnt in preschools and how this contributes to children’s subsequent learning in schools. This paper explores the dilemma of trying to increase preschool children’s learning of mathematics, whilst allowing their play to guide that learning. In Sweden, the revised curriculum for preschools specifies more mathematics to be covered. Yet, like other countries, Sweden traditionally has seen preschools as places where learning arises from children’s play. We suggest two avenues for further research that would contribute information to increasing the likelihood of play supporting mathematics learning.